Although Travis Bickle (Robert DeNiro) has some “bad ideas” in his head, those thoughts aren’t half as frightening as the man who’s thinking them — not because he’s a monster, but because he isn’t. There’s nothing monstrous about him. With his rumpled shirt and friendly manner, he seems … average, just a regular working man who wants his life to have “a sense of someplace to go.” But rejection, isolation and fear do strange, scary things a man, so it doesn’t take long for Travis to construct another reality, one based on paranoia, a thirst for justice, a desire to be heard. And he means to make to make sorry every last person who didn’t care enough to listen.

Doubtless this is where Martin Scorcese’s eerie, savage and deeply unsettling “Taxi Driver” hits the hardest: in showing just how close Travis, a well-meaning loner who wants desperately to connect with anyone, is to his breaking point, and just how close we are to ours. Scorcese and DeNiro are unflinching in their portrayal of Bickle’s slow but completely believable descent into a world of delusions and violence. Both director and actor are painstakingly deliberate in their work, with Scorcese’s every shot providing silent insights into Bickle and DeNiro’s every look and expression — his bizarre smiles are extraordinarily effective — suggesting this quiet man is coming apart at the seams. From the moment the opening credits roll, it’s merely a question of what happens when the last thread gets pulled.

The opening credits, with Michael Chapman’s cinematography and Bernard Herrmann’s haunting score, do much to create the surreal atmosphere and tone of unease in “Taxi Driver.” Glimpsed through the smeary, rain-soaked windshield of a cab, New York City seems like a fresco painting, with all the grayness and the sharp angles blurred together. That togetherness, however, is merely an illusion for Bickle, a Vietnam veteran who takes the night shift as a taxi driver because he can’t sleep nights. “Might as well get paid,” he reasons, and attempts to joke with the personnel officer, who shoots him down. Bickle tries again with Betsy (Cybill Shepherd), a blonde beauty working on a senator’s (Leonard Harris) presidential campaign. She seems interested until he takes her to a pornographic movie on their second date and the relationship comes to a screeching halt. Betsy brushes off every one of his inept but sweetly sincere apologies, and something deep in Bickle’s psyche snaps.

Cleaning up his route — which takes him to the grimiest corners of the city, the ones he wishes he could “flush down the fuckin’ toilet” — becomes his new focus, and he hones in on Iris (Jody Foster), an prepubescent prostitute living under the thumb of Sport (Harvey Keitel), her slimy pimp. Bickle wants to liberate Iris from this life of drugs and smut; she doesn’t want to be rescued (“it saves me from myself,” she calmly explains), and her resistance sends him on a single-minded quest that ends in one of the bloodiest showdowns ever set to celluloid. Filmed in hazy slow motion with an almost tender attention to detail, the sequence is shocking in its brutality. Not once does Scorcese move the camera from the action; in doing this, he smashes down the barrier between audience and screen, forcing us into the gore, blood and gristle. It’s a remarkably effective method that also makes “Taxi Driver” seem like the director’s most personal film (indeed, he has said the movie was one he “had to make”).

The same seems true of DeNiro, who throws himself into Travis Bickle to such an alarming degree we fear for the actor’s safety. “Taxi Driver” is DeNiro’s film, and he owns every inch of it with his startlingly powerful performance. He’s convincing in Bickle’s quieter moments, when he visibly feels the sting of Betsy’s rejection and the degradation of the people he drives, and the later on, when his loneliness shapes into dangerous psychosis. But nowhere is he better than in the movie’s closing moments, where satisfaction and happiness seem within reach. With his eyes, DeNiro deals the final blow, and we know Bickle has made a trip he can’t come back from.